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  • 1
    Electronic Resource
    Electronic Resource
    On partial differential equations related to Lorenz system (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1589-1597 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Partial differential equations are constructed such that a truncation scheme as adopted by Lorenz [J. Atmos. Sci. 20, 130 (1963)] will lead to Lorenz equations. The partial differential equations are much simpler than those of the Rayleigh–Bernard problem and are essentially of the mixed type. Various aspects of the partial differential equations are explored. It is suggested that the switching back and forth between the elliptic and hyperbolic regimes represents the chaotic behavior of the system in the context of partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527465
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A nonlinear study of Kelvin–Helmholtz stability (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 1253-1262 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Kelvin–Helmholtz stability problem is studied by employing the variational method. With the restriction to a single dominant spatial mode, a set of fully nonlinear evolution equations is derived. The limiting states of these evolution equations are discussed and their stability is analyzed. It is found that at the critical point for the linear stability problem, another stable limiting state with finite amplitude appears. A nonlinear sinusoidal wave state is also found. The nonlinear dispersion relation for this wave is derived. The wavenumber of the dominant spatial mode and its evolution with time can also be determined with the aid of the variational method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865008
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  • 3
    Electronic Resource
    Electronic Resource
    Mechanism for instability of fluid flow down an inclined plane (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1145-1148 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The mechanism of the instability of a fluid flowing down an inclined plane is clarified by the recognition that the Reynolds number can also be interpreted as the Froude number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857614
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  • 4
    Electronic Resource
    Electronic Resource
    Elemental mechanisms of hydrodynamic instabilities (1994)
    Springer
    Acta mechanica Sinica 10 (1994), S. 193-202 
    Details
    ISSN: 1614-3116
    Keywords: hydrodynamic instabilities ; negative damping ; negative diffusion ; ellipticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The elemental mechanisms for many hydrodynamic instabilities can be identified as negative damping, negative diffusion or ellipticity. Identifications of some well-known hydrodynamic instabilities are made. Model equations in connection with the instability associated with ellipticity should be studied more extensively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487607
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  • 5
    Electronic Resource
    Electronic Resource
    On hydrodynamic instabilities, chaos and phase transition (1996)
    Springer
    Acta mechanica Sinica 12 (1996), S. 1-14 
    Details
    ISSN: 1614-3116
    Keywords: ellipticity ; hydrodynamic instabilities ; chaos ; phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Ellipticity as the underlying mechanism for instabilities of physical systems is highlighted in the study of model nonlinear evolution equations with dissipation and the study of phase transition in Van der Waals fluid. Interesting results include spiky solutions, chaotic behavior in the context of partial differential equations, as well as the nucleation process due to ellipticity in phase transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02486757
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  • 6
    Electronic Resource
    Electronic Resource
    Some aspects of dynamics of bubbly liquids (1982)
    Springer
    Flow, turbulence and combustion 38 (1982), S. 305-312 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The formulation of dynamics of a liquid containing gas bubbles or vapor bubbles is presented. It is applied to sound waves and one-dimensional flow problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00385960
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  • 7
    Electronic Resource
    Electronic Resource
    Theory of water waves in an elastic vessel (2000)
    Springer
    Acta mechanica Sinica 16 (2000), S. 97-112 
    Details
    ISSN: 1614-3116
    Keywords: water waves ; elastic vessel ; Dragon Wash
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on-set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and numerical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02486701
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  • 8
    Electronic Resource
    Electronic Resource
    Water waves in an elastic vessel (1997)
    Springer
    Acta mechanica Sinica 13 (1997), S. 289-303 
    Details
    ISSN: 1614-3116
    Keywords: water waves ; elastic vessel ; Dragon Wash
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed for the generation of axisymmetric low-frequency gravity waves by the high- frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487188
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  • 9
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    Some aspects of dynamics of bubbly liquids (1982)
    Springer
    Details
    Publication Date: 1982-01-01
    Print ISSN: 1386-6184
    Electronic ISSN: 1573-1987
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Published by Springer
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  • 10
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    A Study of Relaxing Waves (1972)
    American Institute of Physics
    Details
    Publication Date: 1972-11-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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